Results 301 to 310 of about 12,262,956 (340)
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IFAC Proceedings Volumes, 2000
Abstract Some Optimal Control problems can be reduce to problems of Nonlinear Progran1ming. Methods of penalty functions are widely used in Nonlinear Programming. Theorems of the existence of exact penalty parameters for solving of the problems of Nonlinear Programming by the method of exact penalty functions are proved.
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Abstract Some Optimal Control problems can be reduce to problems of Nonlinear Progran1ming. Methods of penalty functions are widely used in Nonlinear Programming. Theorems of the existence of exact penalty parameters for solving of the problems of Nonlinear Programming by the method of exact penalty functions are proved.
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The Generalized Penalty-Function/Surrogate Model
Operations Research, 1973This paper combines the monotonic-penalty-function and surrogate models into a general model called the penalty-function/surrogate model. It unifies and generalizes the central theorems of earlier papers, and provides some new theorems that can be specialized to the Lagrangian penalty-function model (GLM) or to linear surrogates.
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2003
Recall that a relation ≥ defined on a set X is called pre-order if (i) x ≥ x, for all x ∈ X, and (ii) x ≥ y and y ≥ z imply x ≥z. If x ≥ y and y ≥ x, then x and y are called equivalent elements. A pre-order relation is called complete if, for any two elements x and y, either x ≥ y or y ≥ x.
Alexander Rubinov, Xiaoqi Yang
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Recall that a relation ≥ defined on a set X is called pre-order if (i) x ≥ x, for all x ∈ X, and (ii) x ≥ y and y ≥ z imply x ≥z. If x ≥ y and y ≥ x, then x and y are called equivalent elements. A pre-order relation is called complete if, for any two elements x and y, either x ≥ y or y ≥ x.
Alexander Rubinov, Xiaoqi Yang
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Exact penalty functions in nonlinear programming
Mathematical Programming, 1973In this paper some new theoretic results on piecewise differentiable exact penalty functions are presented. Sufficient conditions are given for the existence of exact penalty functions for inequality constrained problems more general than concave and several classes of such functions are presented.
James P. Evans +2 more
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On the exactness of a class of nondifferentiable penalty functions
Journal of Optimization Theory and Applications, 1988We consider a class of non-differentiable penalty functions for the solution of nonlinear programming problems without convexity assumptions. Preliminarily, we introduce a notion of exactness which appears to be of relevance in connection with the solution of the constrained problem by means of unconstrained minimization methods. Then, we show that the
DI PILLO, Gianni, GRIPPO, Luigi
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Second-Order Analysis of Penalty Function
Journal of Optimization Theory and Applications, 2010The authors study global exact penalty properties for general nonlinear programming problems. Global exact penalty properties are conditions under which every global minimum of the original problem is also a global minimum of the penalized problem. The global second-order sufficient conditions are similar to those in [\textit{X. Q. Yang}, Math. Program.
Yang, X. Q., Zhou, Y. Y.
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Penalty function versus non-penalty function methods for constrained nonlinear programming problems
Mathematical Programming, 1971The relative merits of using sequential unconstrained methods for solving: minimizef(x) subject togi(x) ź 0, i = 1, ź, m, hj(x) = 0, j = 1, ź, p versus methods which handle the constraints directly are explored. Nonlinearly constrained problems are emphasized.
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1992
Since the early 1970s, some estimation-type identification procedures have been proposed. They are to choose the orders k and i minimizing $$P(k,i) = {\text{ln}}{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\sigma }}\mathop{{k,i}}\limits^{2} + (k + i)\frac{{C(T)}}{T}$$ , where σ k,i 2 is an estimate of the white noise variance ...
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Since the early 1970s, some estimation-type identification procedures have been proposed. They are to choose the orders k and i minimizing $$P(k,i) = {\text{ln}}{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{\sigma }}\mathop{{k,i}}\limits^{2} + (k + i)\frac{{C(T)}}{T}$$ , where σ k,i 2 is an estimate of the white noise variance ...
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